.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/rotations/rotating_z_to_high_symmetry_directions.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_rotations_rotating_z_to_high_symmetry_directions.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_rotations_rotating_z_to_high_symmetry_directions.py:


=====================================================
Rotating z-vector to high-symmetry crystal directions
=====================================================

This example shows how to sample high-symmetry crystal directions
:math:`\mathbf{t} = [u, v, w]` (or zone axes) using
:meth:`orix.vector.Miller.from_highest_indices`.
We will also return the rotations :math:`R` which rotate
:math:`\mathbf{v_z} = (0, 0, 1)` to :math:`\mathbf{t}`.

We do the following to obtain the high-symmetry crystal directions:

1. Select a point group, here :math:`S = mmm`.
2. Sample all directions :math:`\mathbf{t_i}` with indices of -1, 0, and 1
3. Project :math:`\mathbf{t_i}` to the fundamental sector of the Laue group of :math:`S`
   (which in this case is itself)
4. Discard symmetrically equivalent and other duplicate crystal directions.
   Vectors such as [001] and [002] are considered equal after we make them unit vectors.
5. Round the vector indices to the closest smallest integer (below a default of 20).

The rotations :math:`R` can be useful e.g. when simulating diffraction patterns from
crystals with one of the high-symmetry zone axes :math:`\mathbf{t}` aligned along the
beam path.

.. GENERATED FROM PYTHON SOURCE LINES 26-37

.. code-block:: Python


    from orix.crystal_map import Phase
    from orix.quaternion import Rotation
    from orix.vector import Miller, Vector3d

    phase = Phase(point_group="mmm")
    t = Miller.from_highest_indices(phase, uvw=[1, 1, 1])
    t = t.in_fundamental_sector()
    t = t.unit.unique(use_symmetry=True).round()
    print(t)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Miller (7,), point group mmm, uvw
    [[0. 0. 1.]
     [0. 1. 1.]
     [0. 1. 0.]
     [1. 1. 1.]
     [1. 0. 1.]
     [1. 1. 0.]
     [1. 0. 0.]]




.. GENERATED FROM PYTHON SOURCE LINES 38-40

Get the rotations that rotate :math:`\mathbf{v_z}` to these crystal
directions

.. GENERATED FROM PYTHON SOURCE LINES 40-46

.. code-block:: Python

    vz = Miller(uvw=[0, 0, 1], phase=t.phase)
    R = Rotation.identity(t.size)
    for i, t_i in enumerate(t):
        R[i] = Rotation.from_align_vectors(t_i, vz)
    print(R)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Rotation (7,)
    [[ 1.      0.      0.      0.    ]
     [ 0.9239 -0.3827  0.      0.    ]
     [ 0.7071 -0.7071  0.      0.    ]
     [ 0.8881 -0.3251  0.3251  0.    ]
     [ 0.9239  0.      0.3827  0.    ]
     [ 0.7071 -0.5     0.5     0.    ]
     [ 0.7071  0.      0.7071  0.    ]]




.. GENERATED FROM PYTHON SOURCE LINES 47-49

Plot the crystal directions within the fundamental sector of Laue
group :math:`mmm`

.. GENERATED FROM PYTHON SOURCE LINES 49-60

.. code-block:: Python


    fig = t.scatter(
        vector_labels=[str(vi).replace(".", "") for vi in t.coordinates],
        text_kwargs={
            "size": 15,
            "offset": (0, 0.03),
            "bbox": {"fc": "w", "pad": 2, "alpha": 0.75},
        },
        return_figure=True,
    )
    fig.axes[0].restrict_to_sector(t.phase.point_group.fundamental_sector)



.. image-sg:: /examples/rotations/images/sphx_glr_rotating_z_to_high_symmetry_directions_001.png
   :alt: rotating z to high symmetry directions
   :srcset: /examples/rotations/images/sphx_glr_rotating_z_to_high_symmetry_directions_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.979 seconds)

**Estimated memory usage:**  9 MB


.. _sphx_glr_download_examples_rotations_rotating_z_to_high_symmetry_directions.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: rotating_z_to_high_symmetry_directions.ipynb <rotating_z_to_high_symmetry_directions.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: rotating_z_to_high_symmetry_directions.py <rotating_z_to_high_symmetry_directions.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_